line 1: 2x -y+3z=9
line 2: x+2y+z=8
line3: x-2y +z=0
add last 2 lines...2x+2z=8, or z=4-x
subtrakt line 3 from line2...4y=8, so y=2.........y=2
line 2...x +4 +z=8, so x+z=4, or x=4-z
line 1...2x -2 +3z=9, so 2x=11-3z, so x=(11-3z)/2...=4-z
11-3z=2*(4-z)=8-2z, -z=8-11 =-3, so z=+3......z=3
line 3...x-2*(2) +3=0, x-4+3=0, x-1=0, so z=1